Course in Non Destructive Testing of Wood 02 Acoustics – Pág. 1 ETSI Montes, ETS Arquitectura – Universidad Politécnica de Madrid Madrid, Junio 2005 1 Acoustics of wood Introduction * Acoustical parameters * Stress wave propagation in 1D and 3D * Stress wave velocity, relationship with MOE, MOR, density and fiber length * Practical application: - evaluation of urban trees, defect detection - wood selection for musical instruments
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Course in Non Destructive Testing of Wood 02 Acoustics – Pág. 1ETSI Montes, ETS Arquitectura – Universidad Politécnica de Madrid Madrid, Junio 2005
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Acoustics of wood
Introduction* Acoustical parameters
* Stress wave propagation in 1D and 3D
* Stress wave velocity, relationship with MOE, MOR, density and fiber length
* Practical application: - evaluation of urban trees, defect detection - wood selection for musical instruments
Course in Non Destructive Testing of Wood 02 Acoustics – Pág. 2ETSI Montes, ETS Arquitectura – Universidad Politécnica de Madrid Madrid, Junio 2005
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Acoustic parameters of wood are:- sound velocity,
- acoustic impedance
- damping, logarithmic decrement
Sound velocity in homogeneous solidsvelocity:
Wave forms: longitudinal (pressure)
transverse (shear)
surface
MOE: modulus of elasticityG : shear modulusν : Poisson ratio
Stress wave is the mixture of the 3 wave forms.
νν
++
=1
12,187,0ts VV
( )( )ννν
ρ 2111
−+−
=MOEVl
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Sonic velocities of orthotropicsolids like wood:
Longitudinal (p) waves: V11, V22, V33
Transverse waves V44 =VRTdeduced from V23 and V32
Figure from V. Bucur: Acoustics of wood
Figure from V. Bucur: Acoustics of wood
Longitudinal velocity surface
Velocity depends on the direction of the propagation.
Velocity of the p waves are the highest
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Hankinson’s formula
0
1
2
3
4
5
0 15 30 45 60 75 90Angle (degree)
Velo
city
(km
/s)
Velocity (km/s)Hankinson
L R
V(α)=V0 V90/(V0 sin(α)n+V90 cos(α)n) n=2
Demonstration:
Material: beech veneer
Course in Non Destructive Testing of Wood 02 Acoustics – Pág. 5ETSI Montes, ETS Arquitectura – Universidad Politécnica de Madrid Madrid, Junio 2005
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Attenuation
figure from F. C. Beall article
Acoustic impedance (z) : z=Vρ
zwood⊥= 0,5 MPa s/m
zwood =2,5 MPa s/m zair =0,4 KPa s/m
Reflection coefficient (R) reflected wave energy/ incident wave energy
Wave propagation is perpendicular to the surface:
q=z1/z2 wood
( )( )2
2
11
+−
=qqR
z1
z2
z1>z2
qwood /air=6000
Rwood/air=0,9993 air
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-1
-0,5
0
0,5
1
1,5
0 1 2 3 4 5 6 7
Time
Ae-λt
A1
A2
T
Damping characterisation by the logarithmic decrement (δ)
δ=ln(A1/A2)=λT
δ=ln(a1/a2)/dt/f
Logarithmic decrement determination
a1
a1: amplitude (black)
a2: amplitude at the delayed spectra (white)
dt: delay
f : frequency
spectra
vibration
a1
a2
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Experimental set-up for
logarithmic decrement determination
Sound propagation around knot
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p-Wave propagation around knot in spruce lumber
Grid size is 10 by 10 mm
Pendulum was used for making uniform start signal
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Amplitude
Time
treshold
starter signal
receiver signal
Measured time depends on the receiver signal level
Determination of the stress wave time
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y = 1,8039x + 6,9R2 = 0,9999
0
100
200
300
400
0 50 100 150 200
dis tance [cm]
time
[ µs]
TOF slope technique for velocity determination
Velocity is determined by the slope.
Accurate test
Stress wave velocity, relationship with MOE, MOR, density and fiber length
MOEdynamic= ρ V2
MOEstatic < MOEdynamic (Reason is creep)
Velocity is a good predictor of MOE
MOE and MOR correlation is rather high (0,7-0,8), so transitive there is correlation between V and MOR ( 0,6 - 0,7)
(correlation coefficients are in the brackets)
Effect of time on MOE determination
y = -0,1988x + 9,5186R2 = 0,9875
8,89,09,29,49,69,8
10,010,210,4
-4 -2 0 2 4
log(characteristic time[s])
MO
E[G
Pa]
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Velocity and densityThere is no correlation between velocity in grain direction and density. Foresters in Australia and Japan are predicting density by stress wave velocity perpendicular to the grain.
Velocity and fiber lengthThere is correlation between fiber length and velocity in fiber direction. Longer fibers resulting higher MOE and MOR.
Velocity and microfibril angleThere is correlation between microfibril angle and velocity in fiber direction. Lower angle results higher velocity and MOE
Practical applications:- Predicting tree stiffness
- Evaluation of urban trees, defect detection
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Stiffness grading of trees by stress wave velocity determination
Director ST300 tool
by Fiber-gen, NZ
Background:
MOE= ρV2
Stiffness grading of trees by stress wave velocity determination
TreeSonic tool by
Fakopp and Weyerhaeuser
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Tree evaluation using the stress wave technique
Sound propagates faster in intact than in decayed wood. By simply hitting on the tree and measuring the radial stress waves velocity, internal defects are detectable. Stress waves are generated by hitting the start transducer using a hammer.
Figure shows the sound propagation in an intact and in a decayed tree.
The principle
Course in Non Destructive Testing of Wood 02 Acoustics – Pág. 19ETSI Montes, ETS Arquitectura – Universidad Politécnica de Madrid Madrid, Junio 2005
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FAKOPP Microsecond Timer
Measurement perpendicular to the grain
Evaluation
The evaluation is rather simple. If the measured velocity is lower than 90% of the velocity in an intact tree, the tree contains an internal defect, in the line between the transducers. Is the deviation is higher the defect size is also higher. The relative velocity change (RVC) is a measure of the defect size.
100*reference
measuredreference
VVV
RVC−
=
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Reference velocity examples:
Tree Radial Tree Radialspecies velocity [m/s] species velocity [m/s]
Poplar 1140 Larch 1490Spruce 1410 Oak 1620Silver fir 1360 Beech 1670Scotch fir 1470 Linden 1650Black fir 1480 Maple 1690
Examples:
We are testing big trees.
Poplar trees in a protected area.
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The extention of the decay is the question.
The extention of the decay is the question.
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The extention of the decay is the question.
The extention of the decay is the question.
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A huge plane tree in a play ground
Some defect found by stress wave technique.
Defect was invisible on the outside.
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Acoustic tomography
Using multiple measurements in a plane, 2D imaging of a decay is possible.
Experiment with artificial defect.
Velocity decreases greater than 7% are indicated by bold numbers.
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Self calibration
Self calibration is possible based on the velocity measurement between the neighboring sensors. This direction is near tangential. Wood material close to the bark, between two neighboring sensors is usually healthy, or a defect is visible from outside, like frost vibs. The average of the near tangential velocity data of the healthy sections is the basic reference velocity data.
Ratio of the stress wave velocity measured in different anatomical orientations, relative to the near-tangential direction. Valid for the 6-point setup.
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Acoustic tomographyTypically 6 to 32 acoustic sensors are placed around the tree at the level to be tested. Each sensor is equipped with a spike which is tapped through the bark, into contact with the wood material. A hammer tap on a sensor generates stress waves propagates through the tree, which are received and measured by all the other sensors.
A software takes all of transit time data. Using the distance between sensors, velocity is calculated. The end result is a two dimensional velocity distribution (tomogram) of the tree at the test level.
Decay or cavity appear on the tomogram image.Detecting internal decay by sensors located at the surface is possible, because decay modify the sound propagation.
Sound propagation
Oak disk, grid size is 2 by 2 cm, time resolution is 20 µs.
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Sound propagation in a larch disk
Grid size is 3 by 3 cm, time resolution is 20 µs
20 µs
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40 µs
60 µs
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80 µs
100 µs
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120 µs
140 µs
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160 µs
180 µs
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200 µs
220 µs
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240 µs
260 µs
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280 µs
300 µs
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320 µs
340 µs
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360 µs
Acoustic tomography systems:
- PICUS SONIC TOMOGRAPH - ARBOTOM ®- FAKOPP 2D Timer
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PICUS SONIC TOMOGRAPH
Image source is www.tree-test.com
ARBOTOM®
Image source:
www.rinntech.de
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FAKOPP 2D Timer
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Example images:
Linden and
Nut tree
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Evaluation methods
• Relative line velocity decrease• Cell based backprojection• Filtered backprojection
Relative line velocity decrease
1. Calculate reference velocity from the average of line velocities between neighboring sensors.
2. Select a line between any two sensors as a „defect line” if its velocity is lower than 85% of reference velocity
3. Draw a spot where two defect lines intersecting each other.
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Example image,
Relative line velocity decrease method
Cell based backprojection
1. Divide the area into cells.2. The slowness (reciprocal of velocity) of
each cell is calculated by the average of line slownesses intersecting the cell.
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Example image,
Cell based backprojection
Filtered backprojection
• Theoretical basis by J. Radon in 1917• Used in:
- Medicine (CT, NMR)- Geology- Astronomy- Ocean research- Wood NDT- etc.
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• Radon transform of f(x,y):
• Our case:
where ti,j is the time measured between the ith and jth sensorsXj and Xj are the coordinates of the ith and jth sensorsv(x,y) is the velocity at the (x,y) point
We know ti,j and need v(x,y) => INVERSION
• Solution: projection-slice theorem by Bracewell:connection between Radon and Fourier transform